Once the spacecraft is in its science orbit at the Moon, the lander mission can begin.
While the orbiter doesn’t care much about what phase the Moon is in, the lander and rover need sunlight for warmth and power, so the timing of launch will be dictated by the necessity to get the lander on the ground at its landing site very soon after local dawn.
The lander will fall to the surface, its four lander legs absorbing the shock of landing. The rover will roll out of the lander shortly after the landing in order to make the most of its brief, two-week primary mission. Finally, the Orbiter High Resolution Camera will perform high-resolution imaging of the landing site prior to the lander mission. Officially, the lander mission has an expected lifetime of 14 days, but maybe there is hope that it will survive a lunar night to do science on a second lunar day.
India’s mission landing near the south pole, and China’s landing on farside, will only enhance global understanding of the Moon, regardless of who gets there first.